Respuesta :

To solve the equation

[tex]2x^2-24x+54=0[/tex]

we are going to use the general formula for quadratic equations:

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

In our case a=2, b=-24 and c=54. Then

[tex]\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4(2)(54)}}{2(2)} \\ =\frac{24\pm\sqrt[]{576-432}}{4} \\ =\frac{24\pm\sqrt[]{144}}{4} \\ =\frac{24\pm12}{4} \end{gathered}[/tex]

Then x is:

[tex]\begin{gathered} x=\frac{24-12}{4}=\frac{12}{4}=3 \\ or \\ x=\frac{24+12}{4}=\frac{36}{4}=9 \end{gathered}[/tex]